scholarly journals 1-Dimensional intrinsic persistence of geodesic spaces

2018 ◽  
Vol 12 (01) ◽  
pp. 169-207 ◽  
Author(s):  
Žiga Virk
Keyword(s):  
Fundamental Group ◽  
Critical Point ◽  
Critical Points ◽  
Homology Group ◽  
Geodesic Space ◽  
Geometric Properties ◽  
Underlying Space ◽  
Persistence Properties ◽  
Precise Relationship ◽  
The Relationship

Given a compact geodesic space [Formula: see text], we apply the fundamental group and alternatively the first homology group functor to the corresponding Rips or Čech filtration of [Formula: see text] to obtain what we call a persistence object. This paper contains the theory describing such persistence: properties of the set of critical points, their precise relationship to the size of holes, the structure of persistence and the relationship between open and closed, Rips and Čech induced persistences. Amongst other results, we prove that a Rips critical point [Formula: see text] corresponds to an isometrically embedded circle of length [Formula: see text], that a homology persistence of a locally contractible space with coefficients in a field encodes the lengths of the lexicographically smallest base, and that Rips and Čech induced persistences are isomorphic up to a factor [Formula: see text]. The theory describes geometric properties of the underlying space encoded and extractable from persistence.

The relationship of the scleractinian corals to the rugose corals

Paleobiology ◽  
1980 ◽  
Vol 6 (02) ◽  
pp. 146-160 ◽  
Author(s):  
William A. Oliver
Keyword(s):  
Critical Points ◽  
Scleractinian Corals ◽  
Convincing Evidence ◽  
Early Triassic ◽  
Rugose Corals ◽  
History Of ◽  
The Subject ◽  
Relationship Of ◽  
The Relationship ◽  
Biologic Factors

The Mesozoic-Cenozoic coral Order Scleractinia has been suggested to have originated or evolved (1) by direct descent from the Paleozoic Order Rugosa or (2) by the development of a skeleton in members of one of the anemone groups that probably have existed throughout Phanerozoic time. In spite of much work on the subject, advocates of the direct descent hypothesis have failed to find convincing evidence of this relationship. Critical points are:(1) Rugosan septal insertion is serial; Scleractinian insertion is cyclic; no intermediate stages have been demonstrated. Apparent intermediates are Scleractinia having bilateral cyclic insertion or teratological Rugosa.(2) There is convincing evidence that the skeletons of many Rugosa were calcitic and none are known to be or to have been aragonitic. In contrast, the skeletons of all living Scleractinia are aragonitic and there is evidence that fossil Scleractinia were aragonitic also. The mineralogic difference is almost certainly due to intrinsic biologic factors.(3) No early Triassic corals of either group are known. This fact is not compelling (by itself) but is important in connection with points 1 and 2, because, given direct descent, both changes took place during this only stage in the history of the two groups in which there are no known corals.

The Effects of Drying Techniques on Clay-Rich Soil Texture

1974 ◽  
Vol 32 ◽  
pp. 466-467
Author(s):  
T. G. Naymik
Keyword(s):  
Critical Point ◽  
Liquid Nitrogen ◽  
Liquid Nitrogen Temperature ◽  
Drying Methods ◽  
Air Drying ◽  
Freeze Dried ◽  
Critical Point Drying ◽  
Set Up ◽  
The Relationship ◽  
Quartz Grains

Three techniques were incorporated for drying clay-rich specimens: air-drying, freeze-drying and critical point drying. In air-drying, the specimens were set out for several days to dry or were placed in an oven (80°F) for several hours. The freeze-dried specimens were frozen by immersion in liquid nitrogen or in isopentane at near liquid nitrogen temperature and then were immediately placed in the freeze-dry vacuum chamber. The critical point specimens were molded in agar immediately after sampling. When the agar had set up the dehydration series, water-alcohol-amyl acetate-CO2 was carried out. The objectives were to compare the fabric plasmas (clays and precipitates), fabricskeletons (quartz grains) and the relationship between them for each drying technique. The three drying methods are not only applicable to the study of treated soils, but can be incorporated into all SEM clay soil studies.

Scale-dependent merging of baroclinic vortices

1994 ◽  
Vol 264 ◽  
pp. 81-106 ◽  
Author(s):  
J. Verron ◽  
S. Valcke
Keyword(s):  
Numerical Simulations ◽  
Critical Point ◽  
Lower Layer ◽  
Interaction Mechanism ◽  
Competitive Effects ◽  
Different Types ◽  
Shape Effects ◽  
Baroclinic Vortices ◽  
The Relationship ◽  
Stratified Model

The influence of stratification on the merging of like-sign vortices of equal intensity and shape is investigated by numerical simulations in a quasi-geostrophic, two-layer stratified model. Two different types of vortices are considered: vortices defined as circular patches of uniform potential vorticity in the upper layer but no PV anomaly in the lower layer (referred to as PVI vortices), and vortices defined as circular patches of uniform relative vorticity in the upper layer but no motion in the lower layer (referred to as RVI vortices). In particular, it is found that, in the RVI case, the merging behaviour depends strongly on the magnitude of the stratification (i.e. the ratio of internal Rossby radius and vortex radius). The critical point here appears to be whether or not the initial eddies have a deep flow signature in terms of PV.The specific phenomenon of scale-dependent merging observed is interpreted in terms of the competitive effects of hetonic interaction and vortex shape. In the case of weaker stratification, the baroclinic structure of the eddies can be seen as dominated by a mechanism of hetonic interaction in which bottom flow appears to counteract the tendency of surface eddies to merge. In the case of larger stratification, the eddy interaction mechanism is shown to be barotropically dominated, although interface deformation still determines the actual eddy vorticity profile during the initialization stage. Repulsion (hetonic) effect therefore oppose attraction (barotropic shape) effects in a competitive process dependent on the relationship between the original eddy lengthscale and the first internal Rossby radius.A concluding discussion considers the implications of such analysis for real situations, in the ocean or in the laboratory.

Mechanoreceptor afferent activity compared with receptor field dimensions and pressure changes in feline urinary bladder

1992 ◽  
Vol 70 (11) ◽  
pp. 1457-1467 ◽  
Author(s):  
John W. Downie ◽  
J. Andrew Armour
Keyword(s):  
Contractile Activity ◽  
Bladder Wall ◽  
Afferent Activity ◽  
Intravesical Pressure ◽  
Receptor Field ◽  
Precise Relationship ◽  
Pressure Changes ◽  
The Relationship ◽  
Simple Fashion ◽  
Pressure Receptor

The relationship between vesical mechanoreceptor field dimensions and afferent nerve activity recorded in pelvic plexus nerve filaments was examined in chloralose-anesthetized cats. Orthogonal receptor field dimensions were monitored with piezoelectric ultrasonic crystals. Reflexly generated bladder contractile activity made measurements difficult, therefore data were collected from cats subjected to actual sacral rhizotomy. Afferent activity was episodic and was initiated at different pressure and receptor field dimension thresholds. Maximum afferent activity did not correlate with maximum volume or pressure. Furthermore, activity was not linearly related to intravesical pressure, receptor field dimensions, or calculated wall tension. Pressure–length hysteresis of the receptor fields occurred. The responses of identified afferent units and their associated receptor field dimensions to brief contractions elicited by the ganglion stimulant 1,1-dimethyl-4-phenylpiperazinium iodide (2.5–20 μg i.a.), studied under constant volume or constant pressure conditions, are compatible with bladder mechanoreceptors behaving as tension receptors. Because activity generated by bladder mechanoreceptors did not correlate in a simple fashion with intravesical pressure or receptor field dimensions, it is concluded that such receptors are influenced by the viscoelastic properties of the bladder wall. Furthermore, as a result of the heterogeneity of the bladder wall, receptor field tension appears to offer a more precise relationship with the activity of bladder wall mechanoreceptors than does intravesical pressure.Key words: bladder distension, intravesical pressure, sacral rhizotomy, viscoelasticity.

Phase space correspondence between Jordan and Einstein frames

2021 ◽  
pp. 2150087
Author(s):  
Amin Salehi
Keyword(s):  
Phase Space ◽  
Critical Point ◽  
Critical Points ◽  
Dynamical Behavior ◽  
Cosmological Parameters ◽  
Jordan Frame ◽  
Field Equations ◽  
Theories Of Gravity ◽  
The Stability ◽  
Jordan And Einstein Frames

Scalar–tensor theories of gravity can be formulated in the Einstein frame or in the Jordan frame (JF) which are related with each other by conformal transformations. Although the two frames describe the same physics and are equivalent, the stability of the field equations in the two frames is not the same. Here, we implement dynamical system and phase space approach as a robustness tool to investigate this issue. We concentrate on the Brans–Dicke theory in a Friedmann–Lemaitre–Robertson–Walker universe, but the results can easily be generalized. Our analysis shows that while there is a one-to-one correspondence between critical points in two frames and each critical point in one frame is mapped to its corresponds in another frame, however, stability of a critical point in one frame does not guarantee the stability in another frame. Hence, an unstable point in one frame may be mapped to a stable point in another frame. All trajectories between two critical points in phase space in one frame are different from their corresponding in other ones. This indicates that the dynamical behavior of variables and cosmological parameters is different in two frames. Hence, for those features of the study, which focus on observational measurements, we must use the JF where experimental data have their usual interpretation.

Depressive Disorder in Primary Care

1987 ◽  
Vol 150 (6) ◽  
pp. 737-751 ◽  
Author(s):  
C. V. R. Blacker ◽  
A. W. Clare
Keyword(s):  
Primary Care ◽  
Depressive Symptoms ◽  
Depressive Disorders ◽  
Psychiatric Morbidity ◽  
Depressive Illness ◽  
Psychiatric Disturbance ◽  
Collaborative Studies ◽  
Effect Of Treatment ◽  
Precise Relationship ◽  
The Relationship

Since the pioneering study of psychiatric morbidity in primary care by Shepherdet alin 1966, it has become increasingly apparent that a substantial proportion (between 20% and 25%) of patients consulting their GP are suffering from some form of psychiatric disturbance (Goldberg & Blackwell, 1970; Hoeperet al,1979). The composition of this psychiatric morbidity has been shown to be almost wholly affective in nature and largely mild in degree. In their important review Jenkins & Shepherd (1983) recently summarised the now extensive findings relating to overall minor psychiatric morbidity in primary care. However, recent collaborative studies between psychiatrists and GPs have identified that within this dilute pool of minor disorders, lurks a significant but poorly served population of patients suffering from depressive disorders which are by no means minor in degree. A number of crucial issues regarding this depression in primary care emerge which the present paper aims to review. In particular, how common is it, and how severe? How does it present and what, if any, are its special characteristics? What is the precise relationship between depressive symptoms and depressive illness presenting to the GP and what is the relationship between physical illness and depression? And finally, what is the course and outcome of depression in this setting and what are the indications for and effect of treatment?

scholarly journals FMEA analysis of social and professional competence in monitoring of students’ personal and professional development

2019 ◽  
Vol 8 (4) ◽  
pp. 258-262
Author(s):  
Aleksander Viktorovich Lyalyuk ◽  
Tatiana Leonidovna Shaposhnikova
Keyword(s):  
Professional Development ◽  
Critical Points ◽  
Personal Development ◽  
Scientific Reasoning ◽  
Swot Analysis ◽  
Professional Competence ◽  
Practical Relevance ◽  
Fmea Analysis ◽  
The Relationship

This paper explains that FMEA analysis of students social and professional competence may become an essential component of psychological and pedagogical monitoring, and shows its performance as related to social and pedagogical follow-up of personal and professional development. It is proved that FMEA analysis allows to determine critical points of students social and professional competence development, i.e. to identify, diagnose and forecast the risks of his or her personal and professional development. The relationship between the FMEA analysis of social and professional competence and other components of psychological and pedagogical monitoring is detected (including SWOT analysis of competences and personal and professional qualities). The theoretical relevance of the research results is in the possibility of further scientific reasoning for the issue of personal development in the system of ongoing education, while the practical relevance is in the possibility of the development of innovative systems and techniques for psychological and pedagogical monitoring.

scholarly journals Global Phase Portrait and Bifurcation Diagram for a Multi-Parametric Linear System

2020 ◽  
Vol 55 (4) ◽  
Author(s):  
Jorge Rodríguez Contreras ◽  
Alberto Reyes Linero ◽  
Juliana Vargas Sánchez
Keyword(s):  
Linear System ◽  
Critical Point ◽  
Phase Portrait ◽  
Bifurcation Diagram ◽  
Critical Points ◽  
Global Dynamics ◽  
Parametric Surfaces ◽  
Critical Points At Infinity ◽  
Global Phase Portrait ◽  
The Stability

The goal of this article is to conduct a global dynamics study of a linear multiparameter system (real parameters (a,b,c) in R^3); for this, we take the different changes that these parameters present. First, we find the different parametric surfaces in which the space is divided, where the stability of the critical point is defined; we then create a bifurcation diagram to classify the different bifurcations that appear in the system. Finally, we determine and classify the critical points at infinity, considering the canonical shape of the Poincaré sphere, and thus, obtain a global phase portrait of the multiparametric linear system.

scholarly journals Computing the fundamental group of a higher-rank graph

2021 ◽  
pp. 1-12
Author(s):  
Sooran Kang ◽  
David Pask ◽  
Samuel B.G. Webster
Keyword(s):  
Fundamental Group ◽  
Homology Group ◽  
Klein Bottle ◽  
Fundamental Groups ◽  
The Third ◽  
Higher Rank ◽  
The One ◽  
Standard Presentation

Abstract We compute a presentation of the fundamental group of a higher-rank graph using a coloured graph description of higher-rank graphs developed by the third author. We compute the fundamental groups of several examples from the literature. Our results fit naturally into the suite of known geometrical results about higher-rank graphs when we show that the abelianization of the fundamental group is the homology group. We end with a calculation which gives a non-standard presentation of the fundamental group of the Klein bottle to the one normally found in the literature.

scholarly journals Systemic Sudden Stops: The Relevance of Balance-Sheet Effects and Financial Integration

2016 ◽  
Author(s):  
Guillermo Calvo ◽  
Alejandro Izquierdo ◽  
Luis-Fernando Mejía
Keyword(s):  
Developing Countries ◽  
Critical Point ◽  
Foreign Exchange ◽  
Financial Integration ◽  
Balance Sheet ◽  
Banking System ◽  
Sudden Stop ◽  
Balance Sheet Effects ◽  
Tradable Goods ◽  
The Relationship

Using a sample of 110 developed and developing countries for the period 1990-2004, the chapter claims that a small supply of tradable goods relative to their domestic absorption, and large foreign-exchange denominated debts towards the domestic banking system, denoted Domestic Liability Dollarization, are key determinants of the probability of Systemic Sudden Stop (3S). Moreover, the larger is financial integration, the larger is likely to be the probability of 3S; however, beyond a critical point the relationship gets a sign reversion.

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